The sad, often shocking history of racism in America has produced some of this country's greatest plays, including A Raisin in the Sun, Ma Rainey's Black Bottom, and Clybourne Park. Kirsten Greenidge's Luck of the Irish, now being given its New York premiere at LCT3 at the Claire Tow Theater, doesn't belong in the same class as its predecessors, but the thoughtful and well-intentioned work is a potent reminder of how racial equality has – and has not -- progressed in this country.

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Like Clybourne Park, Luck of the Irish takes place during two time periods in the same house – in this case, in the fictional Boston suburb of Bellington – set 50 years apart. In the 2000s, Hannah (Marsha Stephanie Blake), a harried, married mother struggling with the realities of living in a new town, and her single younger sister, Nessa (Carra Patterson) have just taken ownership of the house they inherited from their grandparents when they are informed that the property may actually belong to longtime neighbors, Joseph and Patty Ann Donovan (played evocatively in the present by Robert Hogan and Jenny O'Hara, and in flashbacks by the equally fine Dashiell Eaves and Amanda Quaid).

Unbeknownst to Hannah and Nessa, the white Irish couple was the home's "ghost buyer," a common practice during a time when African-Americans couldn't legally purchase their own property. And much to sweet-natured Joe's horror, his wife Patty wants it back – although Greendige deftly keeps the mystery of who actually owns the house dangling until play's end.

The scenes set in the 1950s prove to be Greenidge's forte, expertly capturing the uneasy relationship between the two couples, which is charged not only by race, but by financial and class differences. There's a palpable unease in the first meeting between the working-class Donovans and Rex (Victor Williams), a successful doctor, and Lucy (Eisa Davis), a highly educated, well-spoken, and beautifully-dressed woman. A coffee-shop encounter between the two women evolves from bare politeness to outright anger to back-and-forth one-upmanship with lightning speed, while a surprising afternoon tête-à-tête between Lucy and Joe is tinged with a hint of romantic attraction. Throughout the play, Davis is never short of compelling, her outer layer of regality and steel barely covering whatever fear or insecurity is hidden underneath, while Quaid completely embraces Patty's frustration at how badly – and to her mind, unfairly – her life has turned out.

And during the show's conclusion, we watch in almost stunned disbelief as the now-elderly Patty lashes out at Hannah about how the Irish were supposed to have better lives in America than people from other cultures, including African-Americans. At that moment, we realize how Patty is still stuck in the societal order of decades past, never having moved past the "popular wisdom" learned in childhood.

Unfortunately, most of the scenes set in the 2000s, which seem designed to underline Greenidge's point about how racism still exists, suffer from a lack of detail or even mere believability. It's possible that Hannah (passionately embodied by Blake) and her family – including her husband Rich (Frank Harts) and their unseen, unruly child Miles – are actually victims of their white neighbors' prejudice, but it's all tell and no show. Moreover, Hannah too often comes off as paranoid, or at least vaguely deluded about why she might be being shunned. Similarly, much is made of Nessa not receiving a promotion she has not even asked for at a job that is unidentified to the audience. Her behavior seems prompted by low self-esteem, rather than racism.

Rebecca Taichman's fluid direction, which takes maximum advantage of Mimi Lien's effectively minimalist set, does its best to gloss over the script's weaknesses. But not even her skill or the fine work of this ensemble can help make Luck of the Irish a truly great piece of theater.